My paper, “Simultaneous Auctions for Complementary Goods”, grew out of my interest in the motivations for corporate acquisitions and take-overs. The received theory (due especially to Sanford Grossman and Oliver Hart) is that “raiders” acquire mis-managed firms and “turn them around” to make a profit. But my hunch is that, in situations, entrepreneurs acquire well managed, small firms in order to combine them in ways that realize economies of scale or scope. For example, when interstate banking became permitted during the 1990s, there was a wave of bank mergers and acquisitions, many of which involved a dominant bank in one state purchasing smaller banks in neighboring states to become a regional power.

We could model this corporate-acquisition market in terms of a multitude of small-bank owners putting their banks up for auction simultaneously and several larger banks competing to obtain sufficiently many complementary subsidiaries to become dominant in the regional market. It turns out that there is a literature in auction theory regarding optimal noncooperative bidding in an auction for several goods designed to maximize revenue for a single seller who owns all of them. However, it seems that very little attention had been paid to what happens when distinct sellers of complementary objects put their goods on the market without coordinating among themselves. There are significant differences between how these contrasting situations ought to be modeled, and my paper provides a model of simultaneous, non-coordinated auctions that is much more general than its antecedents (formulated in the 1990s) are. I show existence of a monotone pure-strategy Bayesian Nash Equilibrium in simultaneous auctions with private values, which is somewhat surprising relative to what researchers had expected.

As future research, I am interested in applying this model to corporate-takeover markets that I have just described, although I first have to extend my results to a common-values environment to do that.